On the Capacity of the Wiener Phase-Noise Channel: Bounds and Capacity Achieving Distributions

TL;DR

This paper derives tight upper and lower bounds on the capacity of an AWGN channel affected by Wiener phase noise, identifying capacity-achieving input distributions and demonstrating the bounds' accuracy across various SNR levels.

Contribution

It introduces a novel approach to bounding channel capacity with Wiener phase noise and finds explicit, capacity-achieving input distributions through functional optimization.

Findings

Bounds are tight across a wide SNR range.

Capacity-achieving inputs are circularly symmetric and non-Gaussian.

Bounds match known capacities at low and high SNRs.

Abstract

In this paper, the capacity of the additive white Gaussian noise (AWGN) channel, affected by time-varying Wiener phase noise is investigated. Tight upper and lower bounds on the capacity of this channel are developed. The upper bound is obtained by using the duality approach, and considering a specific distribution over the output of the channel. In order to lower-bound the capacity, first a family of capacity-achieving input distributions is found by solving a functional optimization of the channel mutual information. Then, lower bounds on the capacity are obtained by drawing samples from the proposed distributions through Monte-Carlo simulations. The proposed capacity-achieving input distributions are circularly symmetric, non-Gaussian, and the input amplitudes are correlated over time. The evaluated capacity bounds are tight for a wide range of signal-to-noise-ratio (SNR) values, and thus they can be used to quantify the capacity. Specifically, the bounds follow the well-known AWGN capacity curve at low SNR, while at high SNR, they coincide with the high-SNR capacity result available in the literature for the phase-noise channel.